Mark the correct alternative in each of the following:
Let A = {x ϵR : –1 ≤ x ≤ 1} = B. Then, the mapping f : A → B given by f(x) = x |x| is

Question

Mark the correct alternative in each of the following: Let A = {x ϵ R : –1 ≤ x ≤ 1} = B. Then, the mapping f : A → B given by f(x) = x |x| is

Philoid · Accepted Answer

Given that A = {x ϵ R: –1 ≤ x ≤ 1} = B. Then, the mapping f: A → B given by f(x) = x |x|.

For x <0, f(x) <0

⇒ y = -x²

⇒ x = √-y, which is not possible for x > 0.

Hence, f is one-one and onto.

∴ the given function is bijective.

Mark the correct alternative in each of the following:Let A = {x ϵR : –1 ≤ x ≤ 1} = B. Then, the mapping f : A → B given by f(x) = x |x| is